Two Types of Nonlocality in Quantum Mechanics

And How to Resolve Them

Quantum theory is often described as a nonlocal theory, implying the presence of superluminal (faster-than-light) effects, particularly in the context of entangled particles. There are two distinct arguments for this idea of nonlocality.

EPR Nonlocality: This concept originates from the EPR paper, titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” by Albert Einstein, Boris Podolsky, and Nathan Rosen. The authors did not set out to prove that quantum theory is nonlocal; in fact, they considered nonlocality absurd. Instead, they presented what they believed to be a paradox meant to highlight a potential flaw in quantum mechanics. Despite their original intent, the EPR argument is now frequently interpreted as an explanation of how entanglement operates.

Bell Nonlocality: This arises from John Bell’s paper, “On the Einstein Podolsky Rosen Paradox”. Bell expanded on the EPR paradox, introducing his famous theorem to demonstrate that any hidden variable interpretation of quantum mechanics would necessarily involve nonlocal effects.

These two types of nonlocality — EPR and Bell — will be discussed in a bit more detail. Afterward, we will explore how to avoid both interpretations and approach quantum theory in a way that remains fully local.

I wrote an article similar to this before, but it was technical and lengthy. This one is intended to be brief and easier to understand if you have no technical background.

Bell Nonlocality

The uncertainty principle tells us that measuring a particle’s position precisely makes its momentum more uncertain. But what does this uncertainty mean? Does the particle inherently have a momentum that we simply don’t know, or does it lack a definite momentum entirely?

If we assume the particle has a definite momentum that we are ignorant of, this is called a hidden variable theory. In such a theory, properties like momentum (or variables determining it) have real, objective values in ontological reality, but these values are hidden and unknowable to us.

John Bell showed that if reality operates this way, particles must communicate with each other superluminally. A simplified version of his theorem, called the GHZ experiment (by Daniel Greenberger, Michael Horne, and Anton Zeilinger), demonstrates this more directly. The idea involves repeating an experiment with the same initial conditions four times but performing different sets of measurements each time. If the particle’s properties were predetermined, it should be possible to pre-assign the results for all measurements. However, attempts to do so lead to a mathematical contradiction.

You might argue that because the measurement orientations differ, the orientation of the measurement device should be included in the initial conditions. This adjustment can resolve the contradiction by allowing the measuring device’s configuration to influence the outcome.

However, both Bell’s theorem and the GHZ experiment involve systems of multiple particles that are statistically correlated and can be separated by vast distances before measurement. If the measuring device’s configuration influences the outcome, a particle near one device would have to “know” the configuration of a distant device measuring the other particle. This would mean the device’s configuration has a nonlocal effect, transmitting information faster than light.

In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.

— John Bell, “On the Einstein Podolsky Rosen Paradox”

This conclusion only arises if we assume hidden variables exist. Without this assumption, Bell’s theorem doesn’t imply nonlocality. Instead, we avoid pre-assigning values to the particle’s properties altogether, removing the contradiction. This, of course, means that we have to accept that the natural world is nondeterministic.

EPR Nonlocality

If hidden variables are excluded, this implies that certain properties of particles only exist when under certain conditions. For instance, when a particle’s position is measured, it doesn’t just become uncertain whether it has momentum — rather, it doesn’t have momentum at all. Conversely, if its momentum is measured, it gains that property. A particle may gain or lose properties over time depending on what is measured, a process referred to here as realization.

The EPR paper ties realization to certainty (or eigenstates). If we can predict a particle’s momentum with absolute certainty before measuring it, and measurement confirms this prediction, then its momentum must already be realized before measurement. For example, when one particle decays into two particles with opposite spins, conservation of angular momentum ensures that if one particle has positive spin, the other must have negative spin. Quantum theory cannot predict the specific spin of either particle beforehand but guarantees they will be opposite.

Initially, neither particle’s spin is realized because their states are uncertain. Measuring one particle, however, reveals the spin of the other instantly, as the spins are guaranteed to be opposite. Einstein referred to this as “spooky action at a distance” — the idea that measuring one particle’s properties instantaneously realizes those of a distant particle, even across vast distances.

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity…By measuring either [particle], we are in a position to predict with certainty, and without in any way disturbing the second system, either the value of the [position] or the value of [momentum]. In accordance with our criterion of reality, in the first case, we must consider the [position] as being an element of reality; in the second case, the [momentum] is an element of reality.

— Einstein & Podolsky & Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”

This conclusion, however, depends on equating the reality of a property with certainty. If we instead separate mathematical predictions from ontology, we avoid implying any nonlocal effects. Consider a coin with fully known initial conditions: we could predict its flip’s outcome with certainty. However, this certainty doesn’t imply the outcome already exists — it only exists once the coin is flipped. Moreover, certainty remains hypothetical if the coin isn’t flipped at all.

In the relational interpretation of quantum mechanics, a particle’s properties are realized only through physical interaction, and only from the perspective of the interacting systems. When an observer measures a local particle, its properties become realized in their reference frame. This information can be used to predict the distant particle’s properties, but those properties remain unrealized until the observer physically interacts with the distant particle. Thus, realization is inherently local, avoiding any need for nonlocality.